A navigation system is used which measures a position of a vehicle with positioning techniques utilizing artificial satellites and displays map around the vehicle together with the position of the vehicle based on map information stored in advance. The navigation system searches for a route which minimizes a cost to the goal (an arrival time, for example) when the goal is input, displays the searched route on the map, and provides a traveling direction such as right turn and left turn before the vehicle reaches an intersection. The arrival time at the goal largely depends on a situation of traffic of roads. It is possible to predict the arrival time more precisely using traffic information (for example, link travel times, traffic restrictions, traffic jam information, etc.) distributed by road side facilities such as VICS (Vehicle Information and Communication System).
However, the travel time distributed by VICS is a travel time when the vehicle proceeds straight forward at every section (referred to as “link” hereafter). Thus, an excess travel time due to right or left turn (referred to as “a right and left turn cost” hereafter) is not taken into consideration. For example, if the road in a right-turn direction or left-turn direction is busy when the road in a straight forward direction is not busy, time required for the right turn or the left turn becomes longer than a travel time in the straight forward direction. Thus, the travel time predicted using VICS may have reduced accuracy because the right and left turn cost is not taken into consideration.
In this connection, JP patent No. 3591243 (referred to as '243 patent) proposes a technique which attempts to obtain accurate travel time at the right or left turn by calculating the right and left turn cost. FIG. 10A shows a diagram for illustrating the calculation of the time required for the right turn in '243 patent. Each intersection is provided with a terminal apparatus 101 to which a vehicle transmits the travel time whenever it passes through the link. In FIG. 10A, the right and left turn cost is calculated by subtracting the travel time Tb of the vehicle which proceeded straight forward from the travel time Ta of the vehicle which turned right (i.e., Ta−Tb).
Further, JP patent No. 3279009 (referred to as '009 patent) proposes a technique which calculates travel time at the right or left turn by adding the right and left turn cost to the travel time obtained from VICS. FIG. 10B shows a formula for calculating the travel time at the right turn disclosed in '009 patent. In FIG. 10B, the right turn cost is calculated as a function of a flow-in speed in an opposite lane into the intersection and a flow-out speed from the intersection into a lane into which the right turn is performed, each speed is obtained from VICS, and the travel time at the right turn is calculated by correcting the travel time T with the right turn cost and the left turn cost.
However, the right and left turn cost may vary greatly depending on traffic events such as traffic in the opposite lane, visibility of the intersection, etc. Thus, a certain degree of traffic of vehicles which perform right and left turn is necessary in order to precisely recognize the right and left turn cost. In this connection, according to the technique disclosed in '243 patent, it is not possible to precisely calculate the right and left turn cost if the travel time of the intersection which could be included in the route, in the current situation (referred to as real time) under which the arrival time is to be predicted.
Further, the right and left turn cost calculated according to the technique disclosed in '009 patent utilizes the travel time distributed from VICS when the right and left turn cost is calculated. Thus, it is not possible to precisely calculate the arrival time unless the traffic events at the time of calculating the right and left turn cost are approximately the same as the traffic events in real time.
In other words, in order to precisely predict the arrival time reflecting the right and left turn cost, it is desired that the right and left turn cost suited for the traffic events in real time be available. However, conventionally, a technique of recognizing the right and left turn costs reflecting the traffic events in real time does not exist.